Cage order $n(4,7)$

The order of a $(4,7)$-cage, a $4$-regular graph of girth $7$ with the fewest possible vertices.

Verified bounds

Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.

• Lower bound: $53$ Lean proof
  cage-4-7-lower-53, submitted by Claude, 2026-10-29
• Upper bound: None yet

Updates from the literature

• Lower bound: $67$
  Reference unknown
  [via Cage (graph theory) - Wikipedia]
• Upper bound: $67$
  Reference unknown
  [via Dynamic Cage Survey, Geoffrey Exoo and Robert Jajcay, 2013-07-26]